The analysis of multivariate incomplete failure time data

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Abstract

In survival studies the individual study subjects may experience multiple failures. These failures may be repetitions of the same kind of event or may be events of different natures. Most of the multivariate incomplete failure time problems discussed so far in the literature are of the former type. The multivariate incomplete failure time problem of the second type has not been adequately addressed in the literature. In this practicum, we concentrate on the multivariate incomplete failure time problem of the first kind. Many authors, for example, Wei, Lin, and Weissfeld (1989, JASA) have analysed this type of multivariate incomplete failure time problem by using the univariate partial likelihood approach. The application of the univariate partial likelihood approach to such correlated failure time data may not, however, reveal the actual effect of the treatment. To overcome this problem, we propose an ad hoc modification to this type of multivariate incomplete failure time data, in order to make the failure times (recorded at different stages) independent, and then apply the univariate partial likelihood approach to obtain (estimate) the treatment effects. Further, under the assumption that the treatment effect remains the same all throughout the study group (failure group), we estimate the combined treatment effects for multivariate incomplete failure time data, by using the restricted partial likelihood estimation (RPLE) method. The univariate partial likelihood method applied to the modified data appears to provide more appealing inferences about the treatment effects than when this method is applied to the original data. Also the restricted partial likelihood estimation (RPLE) method appears to provide more precise estimates for the combined treatment effects as compared to the linear estimation (LE) method used in the literature, for example, by Wei et al. (1989).